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Quasianalytic Ilyashenko Algebras
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- Journal:
- Canadian Journal of Mathematics / Volume 70 / Issue 1 / 01 February 2018
- Published online by Cambridge University Press:
- 20 November 2018, pp. 218-240
- Print publication:
- 01 February 2018
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- Article
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We construct a quasianalytic field
$\mathcal{F}$ of germs at 
$+\infty $ of real functions with logarithmic generalized power series as asymptotic expansions, such that $\mathcal{F}$ is closed under differentiation and log-composition; in particular, $\mathcal{F}$ is a Hardy field. Moreover, the field 
$\mathcal{F}\,\circ \,\left( -\text{log} \right)$ of germs at 
${{0}^{+}}$ contains all transition maps of hyperbolic saddles of planar real analytic vector fields.
